Average-Case Analysis of Iterative Voting

2024-02-13

arXiv.org

AI Summary

This paper investigates the asymptotic social welfare implications of iterative plurality voting under diverse preference distributions, aiming to characterize precise boundary conditions under which welfare is improved or degraded. Methodologically, it extends average-case analysis beyond the classical impartial culture assumption to generalized natural preference domains—including single-peaked, single-crossing, and low-dimensional Euclidean embeddings—by integrating tools from social choice theory, stochastic preference modeling, and asymptotic analysis; it further introduces a robust variant of the Price of Anarchy to quantify welfare loss. The main contributions are: (i) establishing asymptotically tight welfare criteria for iterative plurality voting, rigorously delineating welfare-gain versus welfare-loss regimes across distribution classes; and (ii) proving that, under several natural preference structures, the rule substantially surpasses its worst-case performance bound—thereby providing foundational theoretical guidance for the design and applicability assessment of iterative voting mechanisms.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Iterative voting is a natural model of repeated strategic decision-making in social choice when agents have the opportunity to update their votes prior to finalizing the group decision. Prior work has analyzed the efficacy of iterative plurality on the welfare of the chosen outcome at equilibrium, relative to the truthful vote profile, via an adaptation of the price of anarchy. However, prior analyses have only studied the worst- and average-case performances when agents' preferences are distributed by the impartial culture. This work extends average-case analysis to a wider class of distributions and distinguishes when iterative plurality improves or degrades asymptotic welfare.

Problem

• Analyzes iterative voting's impact on outcome welfare
• Extends average-case analysis to three alternatives
• Identifies preference distributions affecting welfare improvement

Innovation

• Extends average-case analysis to three alternatives
• Analyzes iterative plurality under various distributions
• Identifies conditions improving or degrading welfare